The approximate value of sqrt[3]{28} is | vedclass

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(B) Let $f(x) = x^{1/3}$. We need to find the value of $f(28)$.Let $x = 27$ and $\Delta x = 1$,so that $x + \Delta x = 28$.We know that $f(x) = x^{1/3

Vedclass · Accepted Answer

$3.037$

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(B) Let $f(x) = x^{1/3}$. We need to find the value of $f(28)$.Let $x = 27$ and $\Delta x = 1$,so that $x + \Delta x = 28$.We know that $f(x) = x^{1/3}$,so $f'(x) = \frac{1}{3}x^{-2/3} = \frac{1}{3x^{2/3}}$.The formula for approximation is $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.Here,$f(27) = (27)^{1/3} = 3$.$f'(27) = \frac{1}{3(27)^{2/3}} = \frac{1}{3(9)} = \frac{1}{27}$.Therefore,$f(28) \approx 3 + \frac{1}{27} 	imes 1$.$f(28) \approx 3 + 0.037037... \approx 3.037$.

The approximate value of $\sqrt[3]{28}$ is

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